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Effect of Roughness Height
The height of the roughness element directly affects the boundary layer development. To study the effect of the roughness height on the profile loss, straight wires with different diameters were tested in both steady and unsteady flow conditions.
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Figure 8. Unsteady boundary layer integral parameters with S-2. |
Figure 9 shows the effect of the diameter of the straight wires placed at 50%S0 on the loss coefficient under unsteady fbw conditions with ф = 0.83 and fr = 0.84. Initially, as the wire diameter is reduced, the loss coefficient decreases. However, as the wire diameter further reduces, the loss increases again at low Reynolds numbers. This is because the loss results from a compromise between the beneficial effect of the bubble size reduction and the calmed region and the negative effect from the earlier formed turbulent flow caused by the wakes. The largest diameter wire induces transition too early and results in a large amount of turbulent fbw. The smallest diameter wire does not induce transition effectively at low Reynolds numbers. Thus, there is an optimum diameter for each flow condition.
In the current study we are mainly interested in the ft)w behaviour at low Reynolds numbers. Figure 10 shows the loss coefficients varying with the diameter of the straight wires at Re=174000 in steady and unsteady ft>w conditions. In the steady flow conditions, the loss coefficient with roughness was reduced significantly compared with that on the smooth surface. The loss continues to decrease as roughness height increases, even for the largest tested wire. However, under the unsteady ft>w conditions, there exits an optimum height. In the current test condition, W-3, which has a relative height of k/S0 = 0.15% or k/S* = 0.62, produces the lowest loss. W-4 (k/S0 = 0.12%, or k/S* = 0.51) was found to produce the lowest loss for Tu=3.5%. Another feature that needs to be noted is that the loss coefficient under unsteady conditions is lower than that in the steady condition if the roughness element is not too high. In this case, the benefit can come from both surface roughness and wake unsteadiness.
Figure 9. Effects of roughness height on Figure 10. Loss coefficients vs. rough-
loss in unsteady conditions ness height at Re=174000
